Data Sufficiency

vladmire wrote:Practice Test 1 question states

How many of the students in a certain class are taking both a history and a science course?

(1) Of all the students in the class, 50 are taking a history course.
(2) Of all the students in the class, 70 are taking a science course.

a. 1
b 2
c both
d either alone
e or neither suff.

Is there enough information to create a venn diagram or a formula. OA - e.

you can do a venn diagram here.
i can't create one within the bounds of a forum post, but imagine that the following post has the form of a venn diagram, with one circle at left and one circle at right.
imagine that the left-hand number is in the left circle but not in the right circle; vice versa for the right-hand number; and that the center number is in the overlapping region of both circles.

let the left-hand circle represent the history class, and the right-hand circle the science class.

in this case, the 2 numbers at left (excluding only the right-hand number) must sum to 50, and the 2 numbers at right (excluding only the left-hand number) must sum to 70.

try different numbers in the middle. it turns out that you can put any number from 0 to 50 (inclusive) in the middle; here are two examples:

30 20 50 (where the '20' is placed first)
40 10 60 (where the '10' is placed first)

since the middle number is queried, this proves that the two statements together are insufficient.